$g(t) = -2t^{2}-t-2(f(t))$ $f(n) = n+6$ $ g(f(-5)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-5)$ . Then we'll know what to plug into the outer function. $f(-5) = -5+6$ $f(-5) = 1$ Now we know that $f(-5) = 1$ . Let's solve for $g(f(-5))$ , which is $g(1)$ $g(1) = -2(1^{2})-1-2(f(1))$ To solve for the value of $g$ , we need to solve for the value of $f(1)$ $f(1) = 1+6$ $f(1) = 7$ That means $g(1) = -2(1^{2})-1+(-2)(7)$ $g(1) = -17$